Noncommutative vortex solitons - art. no. 125010

We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multivortex so lutions. In particular, we prove that the self-dual Bogomol'nyi-Prasad-Somm erfield (BPS) solutions cease to exist once the noncommutativity scale exce eds a critical value. We then study the fluctuation spectra about the stati c configuration and show that the exact non-BPS solutions are unstable belo w the critical value. We have identified the tachyonic degrees as well as m assless moduli degrees. We then discuss the physical meaning of the moduli degrees and construct exact time-dependent vortex configurations where each vortex moves independently. We finally give the moduli description of the vortices and show that the matrix nature of moduli coordinates naturally em erges.